Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
186 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87716 | C2 | semidirect |
| 3. C22×#6014 | C2 | semidirect |
| 4. C22⋊#6014 | C2 | semidirect |
| 5. C22⋊#6014 | C2 | semidirect |
| 6. C4⋊#6014 | C2 | semidirect |
| 7. #11716351 | C2 | semidirect |
| 37. #6014 | D4 | semidirect |
| 50. C22×C25 | M16 | semidirect |
| 100. C25 | #435 | semidirect |
| 154. C22 | #87716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C25 | 2 |
| C2×#87716 | 2 |
| C22×#6014 | 2 |
| C22⋊#6014 | 2 |
| C4⋊#6014 | 2 |
| #11716351 | 2 |
| #65300 | 5 |